spectre.mesh_gen.map2disc

map2disc (BCM) conformal mapping of SPECTRE boundaries to nested interfaces.

The map2disc package provides a 2-D boundary-conformal map (BCM) that maps the unit disc onto an arbitrary poloidal cross-section. By evaluating the map at radii rho = sqrt(tflux) it produces geometrically smooth nested interfaces inside a given plasma boundary.

This module holds the BCM-dependent pieces of mesh generation:

• map_boundary_to_interfaces() — the single, source-agnostic mapping loop. It is also reused by spectre.converters.compute_guesses_map2disc.compute_interface_guesses_map2disc(), which maps a boundary given directly as Fourier-coefficient dicts.

• get_inface_func() / gen_mesh_calc_rz() — build the boundary curve from a live SPECTRE object’s packed state and map it inward.

Both feed map_boundary_to_interfaces() a make_boundary callback — a callable that, given a toroidal angle zeta, returns the boundary curve theta -> (R, Z) at that cross-section.

Conventions are the caller’s responsibility: the negative-theta sign convention and any rescaling of the returned radial gradients into SPECTRE’s s in [-1, 1] coordinate are applied by the caller, not here. This routine works purely in map2disc’s native rho in [0, 1] coordinate.

Module Contents

spectre.mesh_gen.map2disc.map_boundary_to_interfaces(make_boundary, rho_arr, th_arr, zeta_arr, bcm_m, with_grad=False)

Conformally map a boundary inward to nested interfaces using map2disc BCM.

For each toroidal cross-section zeta in zeta_arr the boundary curve is obtained from make_boundary(zeta), a BCM solve is performed, and the map is evaluated on the (rho_arr, th_arr) grid. BCM is a purely 2-D map, so the full 3-D geometry is assembled one zeta slice at a time.

Args:

make_boundary: callable(zeta) -> callable(theta) -> (R, Z); given a

toroidal angle it returns the boundary curve at that cross-section. Returning a per-zeta curve lets the caller do any per-slice setup once instead of on every BCM evaluation.

rho_arr: 1-D array of radial positions in map2disc’s [0, 1] coordinate

(typically sqrt(tflux)); one entry per interface.

th_arr: 1-D array of poloidal angles at which to evaluate the map. The

caller supplies the sign convention (SPECTRE uses negated angles).

zeta_arr: 1-D array of toroidal angles (one field period is sufficient). bcm_m: number of Fourier modes used by the BCM solver. with_grad: if True also return the radial gradients dR/drho and

dZ/drho in map2disc’s rho coordinate.

Returns:

(R_arr, Z_arr) when with_grad is False, otherwise (R_arr, Z_arr, dRdrho_arr, dZdrho_arr). Every array has shape (len(rho_arr), len(zeta_arr), len(th_arr)).

Raises:

ImportError: if map2disc is not installed.

spectre.mesh_gen.map2disc.get_inface_func(xin, test, zeta, inface)

Build the boundary curve of one SPECTRE interface at a fixed toroidal angle.

Unpacks the interface Fourier coefficients from the packed state vector xin and returns a callable theta -> (R, Z) evaluating interface inface of the SPECTRE object test at the toroidal angle zeta.

Args:

xin: packed interface state vector (see spectre.utils.unpack_interfaces()). test: a live SPECTRE object providing geometry and mode metadata. zeta: toroidal angle at which to evaluate the cross-section. inface: interface index (0 <= inface <= mvol - 1).

Returns:

callable(theta) -> (R, Z) evaluating the interface curve.

Raises:

RuntimeError: if inface is out of range.

spectre.mesh_gen.map2disc.gen_mesh_calc_rz(xin, test, inface, bcm_m, rho_arr, th_arr, zeta_arr)

Conformally map a SPECTRE interface inward, returning R, Z and radial gradients.

Thin wrapper around map_boundary_to_interfaces() that uses interface inface of the SPECTRE object test as the mapping boundary. The returned gradients are in map2disc’s rho in [0, 1] coordinate; callers feeding SPECTRE’s s in [-1, 1] coordinate must rescale them (see spectre.mesh_gen.generators.gen_mesh_external()).

Args:

xin: packed interface state vector. test: a live SPECTRE object. inface: interface index used as the mapping boundary. bcm_m: number of Fourier modes for the BCM solver. rho_arr: radial positions in map2disc’s [0, 1] coordinate. th_arr: poloidal angles (SPECTRE’s negated-theta convention). zeta_arr: toroidal angles.

Returns:

(R_arr, Z_arr, dRdrho_arr, dZdrho_arr), each of shape (len(rho_arr), len(zeta_arr), len(th_arr)).